Elevation from Grade and Distance

This is the single most-used line of arithmetic on a construction site: take a known elevation, walk a measured horizontal distance, and add the grade times that distance. Sign discipline is everything — enter a fall as a negative grade and the formula keeps track for you. It is the same relation that sets pipe inverts: an 8 in sanitary lateral run at −2.0 % from an invert of 253.40 m over 42 m arrives at 253.40 − 0.84 = 252.56 m, and if the downstream structure was built at 252.70 the pipe will not drain and someone is coming back with a saw.

Solved for G it becomes the as-built check — measure both ends, divide the difference by the run — and solved for L it answers the layout question, "how far out do I stake the daylight point?" A worked example: a 1.5 % crowned road starting at 431.20 ft crown elevation reaches 431.20 + 1.5 × 260/100 = 435.10 ft at station 2+60. The trap is using the taped slope distance for L instead of the horizontal projection; on flat grades the error hides, on steep ones it does not.